One way to do this is to use prime numbers for the denominators. The first 20 primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
The numerators for these can be the denominator plus 1, that is:
3/2, 4/3, 6/5, etc., which are all improper fractions.